Question 6) Oil and gas exploration companies find new underground deposits by measuring (with incredible precision) the value of g at the Earth's surface.
EXTRA INFO GIVEN:
The challenge: F=Gm1m2/r^2 ONLY works for two cases: point masses, or if one of the masses has spherical symmetry (remember our discussions in class about the force of gravity due to a hollow shell.) For the case of a mass with spherical symmetry, the "r" refers to the distance bewteen the CENTRE of the two masses. That is why when you calculate the gravity on a space ship 300 km above the surface of the Earth, you use r=Re+300 km (where Re is the radius of the Earth).
The mass in the oil pocket problem does NOT have spherical symmetry but can you break it into smaller problems, each of which does have spherical symmetry.
E.g: 1) can you find the force of gravity if the Earth was a solid sphere with uniform density? Look up the radius of the Earth and its mass.
2) can you find the force of gravity from rock (with the density of the Earth) shaped like a sphere with radius 0.5 km that centre is 1 km away from you?
3) can you find the force of gravity from a sphere of oil with radius 0.5 km that centre is 1 km away from you?
4) considering these three results, how do you now answer the question asked? [Hint: do NOT just add all three forces together!.
One other point, in class all of you had no problem determining the density of the Earth (total mass/total volume). In the drop-in centre, some students did not realize that this allowed them to find the mass of any shape of rock (with volume V): M =density * V, where density can be found from total Mass/total Volume